YES
Time: 0.016

Problem:
 Equations:
  fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
  fAC(x3,x4) -> fAC(x4,x3)
  fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
  fAC(x4,x3) -> fAC(x3,x4)
 TRS:
  fAC(x,one()) -> x
  fAC(i(x),x) -> one()
  phi(one(),y1) -> y1
  phi(y1,phi(y2,x)) -> phi(fAC(y1,y2),x)

Proof:
 AC-KBO Processor:
  precedence:
   fAC > phi ~ i ~ one
   weight function:
    w0 = 1
    w(one) = 12
    w(i) = 10
    w(phi) = 1
    w(fAC) = 0
   problem:
    Equations:
     fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
     fAC(x3,x4) -> fAC(x4,x3)
     fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
     fAC(x4,x3) -> fAC(x3,x4)
    TRS:
     
   Qed